$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 5x - 4$ and $ BC = 3x + 8$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {5x - 4} = {3x + 8}$ Solve for $x$ $ 2x = 12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 5({6}) - 4$ $ BC = 3({6}) + 8$ $ AB = 30 - 4$ $ BC = 18 + 8$ $ AB = 26$ $ BC = 26$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {26} + {26}$ $ AC = 52$